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The meteorology data assimilation applications often encounter variational problems with unknown weights, where the corresponding Euler equation is an elliptic partial differential equation. This research focused on retrieving the weights in remote sensing data assimilation by means of the computer-friendly form of the Green’s function obtained by eigenfunction expansion for the boundary value problem of the static Klein–Gordon equation on a rectangular region. With the help of the proposed retrieving method, the assimilation problem of estimating regional precipitation with weather radar and rain-gauge is solved in the Green’s function method. Results show that high accuracy of the proposed method makes it a good candidate for data assimilation problems in operational use.

Green’s Function for Static Klein–Gordon Equation Stated on a Rectangular Region and Its Application in Meteorology Data Assimilation